Semi-classical states for the nonlinear Choquard equations: existence, multiplicity and concentration at a potential well

Silvia Cingolani, Kazunaga Tanaka

We study existence and multiplicity of semi-classical states for the nonlinear Choquard equation: $$ -\varepsilon^2Δv+V(x)v = \frac{1}{\varepsilon^α}(I_α*F(v))f(v) \quad \hbox{in}\…